The Heisenberg antiferromagnet with an easy-plane anisotropy is discussed in which a magnetic spiral is induced by Dzyaloshinskii-Moriya interaction and/or frustration of the exchange coupling. The distortion of the spiral by small in-plane magnetic field is described analytically. It is found that the field can gradually change the vector of the magnetic structure ${\mathbf{k}}_0$ and can produce transitions between phases with incommensurate and commensurate magnetic orderings when ${\mathbf{k}}_0$ is close to $\mathbf{g}/n$, where $\mathbf{g}$ is a reciprocal-lattice vector and $n$ is integer. Analytical expressions for critical fields are derived for $n=2$, 3, and 4. Application of the theory to the triangular-lattice compound $\mathrm{RbFe}{\left({\mathrm{MoO}}_4\right)}_2$ is discussed alongside its potential applicability to other materials. As a by-product of the main consideration, model parameters are found which describe more accurately the full set of available experimental data suggested before for $\mathrm{RbFe}{\left({\mathrm{MoO}}_4\right)}_2$.

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• Dzyaloshinskii-Moriya interaction
• Frustrated magnetism
• Magnetic anisotropy
• Magnetic order
• Magnetic phase transitions
• Magnetism
• Spin waves
• Antiferromagnets
• Helimagnets
• Quantum spin models
• Triangular lattice
• Holstein-Primakoff method
• Methods in magnetism